Investigators say Donnel Jackson killed Troy Wolff and injured his girlfriend, Kristin Ito, in the random knife attack.
Police say Jackson is schizophrenic, and on Monday McGinn said the city needs to do more to address mental illness.
As for Jackson, a judge decided to hold him on $2 million bail, saying his alleged crimes have rattled the community's sense of safety. Jackson declined to go before the judge and let his attorney do the talking.
Assistant Seattle Police Chief Nick Metz joined McGinn to talk about changes they are proposing.
"This, to me, was an extremely shocking event," Metz said.
Among other changes, McGinn said the police department needs more officers.
"We will be reporting to you later what this budget has in it in regards to police officers, and we will be making additional investments," he said.
McGinn also plans to push state lawmakers to fund more treatment beds, so mentally ill patients can be evaluated and helped instead of left on the streets.
"In the city of Seattle we are not going to wait for Olympia," McGinn said. "We will continue pushing them."
Friday's stabbing evokes memories of other incidents, including the murder of Seattle fire captain Stanley Stevenson in 1997 as his family left a Mariners game at the Kingdome. More recently, Seattle police gunned down a man with mental problems in Magnolia.
King County Prosecutor Dan Satterberg has long called for changes in the mental health system, saying what's in place now doesn't work.
"The street is no place to get better if you are mentally ill, and it's a place where people get much much worse," he said.
McGinn plans to convene a summit with the Downtown Seattle Association and others to talk about what can be done to identify and help mentally ill people who are on the streets and in crisis.
He said any solution is bound to cost more money, which could translate into new fees or taxes.
Ito remains at Harborview Medical Center, but her condition has been upgraded to satisfactory.